DETERMINATION OF MIDGAP DENSITY OF STATES IN a-Si : H USING SPACE-CHARGE-LIMITED CURRENT MEASUREMENTS

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DETERMINATION OF MIDGAP DENSITY OF STATES IN a-Si : H USING

SPACE-CHARGE-LIMITED CURRENT MEASUREMENTS

W. den Boer

To cite this version:

W. den Boer. DETERMINATION OF MIDGAP DENSITY OF STATES IN a-Si : H USING SPACE-

CHARGE-LIMITED CURRENT MEASUREMENTS. Journal de Physique Colloques, 1981, 42 (C4),

pp.C4-451-C4-454. �10.1051/jphyscol:1981494�. �jpa-00220951�

JOURNAL DE PHYSIQUE

Colloque C4, suppldment au nOIO, Tome 42, octobre 1981 page C.4-45 1

DETERMINATION OF MIDGAP DENSITY OF STATES IN a-Si:H USING SPACE- CHARGE-LIMITED CURRENT MEASUREMENTS

W. den Boer

Delft University o f Technology, t h e Netherlands

A b s t r a c t . - The d e n s i t y of s t a t e s i n glow d i s c h a r g e d e p o s i t e d amorphous s i l i - con h a s been deduced from space-charge-limited (SCL) c u r r e n t measurements on samples w i t h an n+-i-nf sandwich c o n f i g u r a t i o n . The temperature and f i l m - t h i c k n e s s d e p e n d e n c e o f t h e S c L c u r r e n t a r e found t o be c o n s i s t e n t w i t h t h e t h e o - r y of o n e - c a r r i e r s t e a d y - s t a t e SCL c u r r e n t flow. The r e s u l t i n g midgap d e n s i t y of s t a t e s i s 1 0 ~ ~ - 4 . 1 0 ~ ~ cm-3 .V-'in t h e energy r e g i o n 0.75 t o 0.6 eV below t h e conduction band edge. T h i s f i g u r e i s lower t h a n t h a t u s u a l l y found by t h e f i e l d - e f f e c t t e c h n i q u e (-1017 cm-3 e v - l )

,

probably due t o t h e i n c l u s i o n of i n - t e r f a c e s t a t e s i n f i e l d - e f f e c t measurements.

I n t r o d u c t i o n . - Much i n f o r m a t i o n on t h e q u a l i t y and p r o p e r t i e s of hydrogenated amor-

- -

phous s i l i c o n (a-Si:H) can be o b t a i n e d from i t s d i s t r i b u t i o n of l o c a l i z e d s t a t e s . The method most widely used t o measure t h e d e n s i t y of s t a t e s (DOS) i n a-Si a l l o y s i s t h e f i e l d - e f f e c t t e c h n i q u e [ 1 , 2 ] . This method does n o t d i s t i n g u i s h between i n t e r f a c e s t a t e s a t t h e semiconductor-insulator i n t e r f a c e and bulk s t a t e s and consequently pro- v i d e s an upper l i m i t f o r t h e bulk DOS (1017 cm-3 ev-' f o r a-Si:H). Deep l e v e l t r a n s - i e n t spectroscopy, on t h e o t h e r hand, i s assumed t o measure t h e t r u e bulk DOS and ap- p l i c a t i o n of t h i s t e c h n i q u e on a-Si:H h a s r e s u l t e d i n a midgnp DOS below 1 0 l ~ c m - ~ ev-l [31.

Recently d a r k forward c u r r e n t - v o l t a g e measurements on a-Si:H Schottky d i o d e s have been i n t e r p r e t e d a s g i v i n g evidence f o r space-charge-limited (SCL)current flow [41.

A q u a s i - e x p o n e n t i a l DOS was deduced from t h e s e experiments. The SCL c u r r e n t t e c h n i - que i s a well-known method f o r determining t r a p d i s t r i b u t i o n s i n high r e s i s t i v i t y

s o l i d s and h a s been a p p l i e d t o a l a r g e v a r i e t y of m a t e r i a l s [5].

We propose t o u s e a sandwich s t r u c t u r e w i t h two ohmic c o n t a c t s t o measure SCL cur- r e n t flow. I n t h i s c o n f i g u r a t i o n t h e I - V - c h a r a c t e r i s t i c i s n o t obscured by exponen- t i a l behaviour f o r low v o l t a g e s a s i n t h e c a s e of Schottky d i o d e s . Consequently t h e SCL c u r r e n t regime can be extended t o lower v o l t a g e s .

Theory.- S i n c e undoped a-Si:H i s s l i g h t l y n-type and t h e c o n t a c t s i n a n n+-i-n+

s t r u c t u r e a r e blocking f o r h o l e s , t h e SCL c u r r e n t i s predominantly c a r r i e d by e l e c - t r o n s . Then, under t h e a d d i t i o n a l assumptions t h a t q u a s i - e q u i l i b r i u m e x i s t s , t h a t d i f - f u s i o n c u r r e n t s a r e n e g l i g i b l e and t h a t t h e ohmic c o n t a c t i s an i n f i n i t e r e s e r v o i r of e l e c t r o n s , t h e t h e o r y f o r o n e - c a r r i e r s t e a d y - s t a t e SCL c u r r e n t flow i s a p p l i c a b l e

[ 5 ] . F i r s t we c o n s i d e r a q u a s i - e x p o n e n t i a l d i s t r i b u t i o n of s t a t e s : E-Ec

N ( E ) =

!k

eXp (P) t

t kTt kT

where Nt and Tt a r e parameters c h a r a c t e r i z i n g t h e t r a p d i s t r i b u t i o n and E i s t h e energy of t h e conduction band edge. For t h i s d i s t r i b u t i o n t h e c u r r e n t - d e n s i t y - v o l - t a g e (j-V) c h a r a c t e r i s t i c i s l i n e a r on a log-log-scale, i . e . j--Vm, with m>2.

N, and T, a r e deduced from t h e j - V - c h a r a c t e r i s t i c 151:

where N i s t h e e f f e c t i v e d e n s i t y of s t a t e s a t t h e conduction band edge, pn i s t h e

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981494

C4-452 JOURNAL DE PHYSIQUE

f r e e e l e c t r o n m o b i l i t y , L i s t h e sample t h i c k n e s s , s s i s t h e semiconductor permit- t i v i t y and T

1 = t .

T

I n g e n e r a l a s t r a i g h t - l i n e f i t t o t h e l o g j-log V - c h a r a c t e r i s t i c i s n o t pos,sible.

The DOS can t h e n be e s t i m a t e d by u s i n g t h e f o l l o w i n g a n a l y s i s .

The c o n c e n t r a t i o n of f i l l e d e l e c t r o n t r a p s i n e q u i l i b r i u m i s n

.

When a v o l t a g e i s

t , O

a p p l i e d t h e Fermi-level i s r a i s e d from i t s e q u i l i b r i u m v a l u e E t o EFn due t o space F0

charge i n j e c t i o n from t h e ohmic c o n t a c t . The c o n c e n t r a t i o n of f i l l e d e l e c t r o n t r a p s t h e n becomes nt. Assuming t h a t t h e t r a p d i s t r i b u t i o n N (E) i s continuous and o n l y

t slowly v a r y i n g , n -n can be approximated by

t t , a

n t - n t , o z

F

N t ( E ) dB. ( 3 )

E ~ o

To s i m p l i f y t h e a n a l y s i s we assume t h a t t h e i n j e c t e d c h a r g e i s uniformly d i s t r i b u t e d a c r o s s t h e f i l m a n d t h a t t h e e l e c t r i c f i e l d i s c o n s t a n t and e q u a l t o throughout t h e

f i l m . L

These two assumptions a r e c o n t r a d i c t o r y , b u t it can be shown [ 5 ! t h a t t h i s s i m p l i f i - c a t i o n o v e r e s t i m a t e s t h e DOS by n o t more t h a n a f a c t o r of 2.

The i n j e c t e d c h a r g e Q p e r u n i t a r e a i s t h e n e q u a l t o

W .

S i n c e t h e t r a p d e n s i t y i s much l a r g e r t h a n t h e f r e e e l e c t r o n d e n s i t y most of t h e L i n - j e c t e d c h a r g e i s t r a p p e d , i . e .

Taking two p o i n t s ( j l , V 1 ) and(j2,Vz) on t h e measured j-V-curve we c a l c u l a t e t h e Fermi-level s h i f t AEF=EF2-EF1 corresponding t o a v o l t a g e change AV=V -V

2 1 - AE i s deduced from t h e c u r r e n t - d e n s i t y e q u a t i o n s

F --

where nl and n2 a r e t h e f r e e c a r r i e r d e n s i t i e s a t a p p l i e d v o l t a g e s V1 and V 2' r e s p e c t i v e l y :

E c - E ~ l )

n1 = Nc exp (-

7

E -E c F2

n2 = Nc exp ( -

-

kT ) Then, from (5) and ( 6 ) ,

Using ( 3 ) and ( 4 ) , we c a n w r i t e :

The i n t e g r a l i n (8) can be approximated by

W

where N i s t h e average t r a p d e n s i t y between EF1 and EF2.

t

Then, from ( 8 ) and ( 9 )

,

Experimental.- The f i l m s were grown i n an r f glow d i s c h a r g e of s i l a n e a t a s u b s t r a t e temperature of 300°C. For t h e -50 m t h i c k n+ l a y e r 1 % phosphine was added t o t h e si- l a n e . With t h e s e f i l m s s o l a r c e l l s w i t h e f f i c i e n c i e s exceeding 4 % have been produced

[6]. Quartz o r g l a s s p l a t e s with evaporated chromium s t r i p e s were used a s s u b s t r a t e s . A s upper e l e c t r o d e s chromium-gold s t r i p e s were evaporated p e r p e n d i c u l a r t o t h e lower e l e c t r o d e s , t h e o v e r l a p p i n g a r e a ( l mm2 o r 4 mm2 ) d e f i n i n g t h e d e v i c e .

X e s u l t s and d i s c u s s i o n . - The c u r r e n t d e n s i t y was found t o be independent of d e v i c e a r e a (1 mmL o r 4 mmL ) , which e l i m i n a t e s edge e f f e c t s . The a p p l i e d e l e c t r i c f i e l d should n o t exceed - 5 . 1 0 ~ V/cm. A t h i g h e r f i e l d s t h e f r e e c a r r i e r d e n s i t y i s n o t o n l y i n c r e a s e d by space-charge i n j e c t i o n , b u t a l s o by f i e l d i o n i z a t i o n o u t of t r a p s [ 7 ] .

The temperature dependence of t h e j-V-curves i s i l l u s t r a t e d i n Fig. 1 f o r a r e - p r e s e n t a t i v e sample w i t h an undoped l a y e r t h i c k n e s s of 0.55 pm.

The t r a p d e n s i t y was c a l c u l a t e d f o r t h e c u r v e s measured a t T=251 K, 290 K and 375 K, u s i n g e q u a t i o n s ( 7 ) and ( 1 0 ) . The p o s i t i o n of t h e Fermi-levels was c a l c u l a t e d from ( 5 ) and ( 6 ) , t a k i n g a v a l u e of 1021 (cm V s e c ) - ' f o r t h e pnNc product

[a].

The r e s u l t i n g d e n s i t y of s t a t e s i s r e p r e s e n t e d i n Fig. 2. For e n e r g i e s between 0.75 and 0.6 eV below t h e conduction band edge t h e c a l c u l a t e d N+(E) i s i n t h e range

F i g . 1 : j-V-curves a t t h e i n d i c a - t e d t e m p e r a t u r e s f o r a sample w i t h undoped l a y e r t h i c k n e s s L=0.55 pm.

C4-454 JOURNAL DE PHYSIQUE

-The DOS h a s a l s o been c a l c u l a t e d by t a k i n g t h e b e s t s t r a i g h t l i n e f i t s f o r t h e l o g j- l o g V-curves a t 251 K, 290 K and 375 K and u s i n g e q u a t i o n ( 2 ) . The r e s u l t i n g exponent- i a l d i s t r i b u t i o n s a r e shown i n F i g . 3 and a r e i n r e a s o n a b l e agreement w i t h t h e r e - s u l t s of F i g . 2.

Equation ( 2 ) shows t h a t t h e SCL c u r r e n t s t r o n g l y depends on t h e undoped l a y e r t h i c k - ness L. A s an a d d i t i o n a l check on t h e v a l i d i t y of t h e method t h e DOS has been c a l c u -

l a t e d f o r samples w i t h d i f f e r e n t v a l u e s of L. F i g . 4 shows t h e DOS c a l c u l a t e d f o r samples w i t h L=0.55, 1.1 and 2.45 pm, measured a t T=290 K. The DOS i s v i r t u a l l y i n - dependent of sample t h i c k n e s s .

Fig. 3 : D e n s i t i e s of s t a t e s c a l c u l - F i g . 4 : D e n s i t i e s of s t a t e s c a l c u l - a t e d f o r t h r e e c u r v e s of Fig. 1 a t a t e d f o r t h r e e d i f f e r e n t samples w i t h T=251, 290 and 375 K. The c a l c u l a t - undoped l a y e r t h i c k n e s s L=0.55, 1.1 i o n s a r e based on e q u a t i o n s (1) and ( 2 ) . and 2.45 pm. The measuring tempera-

t u r e was 290 K. C a l c u l a t i o n s a r e based on e q u a t i o n s ( 7 ) and ( 1 0 ) .

I n summary, a midgap d e n s i t y o f l o c a l i z e d s t a t e s i n a-Si:H of -1016 e ~ - l c m - ~ h a s been deduced from SCL currentmeasurements. The d e p e n d e n c e o f t h e S C L c u r r e n t onsample t h i c k n e s s and temperature i s i n r e a s o n a b l e agreement w i t h t h e o r y . The c a l c u l a t e d DOS i s supposed t o r e p r e s e n t t h e t r u e bulk DOS. T h e r e f o r e , we argue t h a t t h e SCL c u r r e n t t e c h n i q u e p r o v i d e s a more r e l i a b l e e s t i m a t e of t h e bulk DOS i n a-Si:H t h a n t h e f i e l d - e f f e c t r e s u l t s i n which i n t e r f a c e s t a t e s a r e l i k e l y t o dominate.

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[6] Ondris, M. and Den Boer, N., Proceedings of t h e T h i r d E.C. P h o t o v o l t a i c S o l a r Energy Conference, Cannes 1980, p. 809.

171 C a r l s o n , D.E. and ~ 7 r o n s k i , C.R., Amorphous Semiconductors, e d i t e d by M.H.

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